The simplex-simulated annealing approach to continuous non-linear optimization
Abstract An algorithm suitable for the global optimization of nonconvex continuous unconstrained and constrained functions is presented. The scheme is based on a proposal by Press and Teukolsky ( Comput. Phys. 5 (4), 426, 1991) that combines the non-linear simplex and simulated annealing algorithms. A non-equilibrium variant will also be presented, whereby the cooling schedule is enforced as soon as an improved solution is obtained. The latter is shown to provide faster execution times without compromising the quality of the attained solutions. Both the algorithm and its non-equilibrium variant were tested with several severe functions published in the literature. Results for nine of these functions are compared with those obtained employing a robust adaptive random search method and the Nelder and Mead simplex method ( Comput. J. 7 , 308, 1965). The proposed approach is shown to be more robust and more efficient in what concerns the overcoming of difficulties associated with local optima, the starting solution vector and the dependency upon the random number sequence. The results obtained reveal the adequacy of the algorithm for the global optimization of a broad range of problems encountered in chemical engineering practice.
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